Equal Responsibility in the Queueing Problem

This is a double seminar.

Title: Pairwise Gain-Splitting Rules in the Reordering Problem (joint work with Youngsub Chun)

Abstract

In the reordering problem, this paper investigates the implications of invariance of relative position, which requires that, for any two problems with the same vector of unit waiting costs, each agent who holds the same relative position with others in the initial queues of these two problems should receive the same net utility in both. We show that the family of all pairwise gain-spliting rules is the maximal set of rules satisfying queue-efficiency, budget balance, individual rationality from an efficient initial queue and Pareto indifference, together with invariance of relative position. Moreover, by replacing individual rationality from an efficient initial queue with individual rationality and imposing independence of smaller costs (respectively, independence of larger costs), we characterize the maximum price rule (respectively, the minimum price rule).

Keywords: Maximum price rule; minimum price rule; pairwise gain splitting rules; reordering problems; split core

16:00-17:00 Youngsub Chun (Seoul National University, South Korea)
Title: Equal Responsibility in the Queueing Problem (joint work with Changyong Han and Ching-Jen)

Abstract

In the context of the queueing problem, we investigate fair compensation through the lens of individual responsibility. Our fairness approach is grounded in the principle that certain groups of agents bear equal responsibility for changes in economic environments and should therefore be affected by the same magnitude. To formalize this idea, we introduce equal responsibility axioms, which require that any change in an agent’s unit waiting cost must lead to a uniform adjustment in the transfers of either all preceding agents or all following agents. We propose a family of equally responsible transfer rules and provide characterizations of this family based on efficiency, Pareto indifference, equal treatment of equals, and either preceding-cost equal responsibility or following-cost equal responsibility. To further refine our analysis, we impose additional axioms that define notable subfamilies, specifically the linear transfer rules and the convex transfer rules, which capture different ways of structuring compensation adjustments. Furthermore, within this family, we identify three distinguished transfer rules - the minimal transfer rule, the maximal transfer rule, and the average transfer rule - each offering a unique perspective on the distribution of responsibility and fairness in queueing. Joint paper with Changyong Han and Ching-Jen Sun.

Keywords: Queueing problem, Equal responsibility, Equally responsible transfer rules, Minimal transfer rule, Maximal transfer rule, Average transfer rule, Axiomatic characterizations.